Transverse heterogeneity effects in the dissipation-induced instability of a horizontal porous layer

The linear stability of a parallel flow in a heterogeneous porous channel is analyzed by means of the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as, by the boundary conditions. A horizontal porous layer bounded by impermeable and infinitely wide walls is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against oblique rolls is studied. The eigenvalue problem is solved numerically.